Issue |
Europhys. Lett.
Volume 63, Number 4, August 2003
|
|
---|---|---|
Page(s) | 512 - 518 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2003-00561-8 | |
Published online | 01 November 2003 |
Short-period attractors and non-ergodic behavior in the deterministic fixed-energy sandpile model
1
Dipartimento di Energetica “S. Stecco” - Via S. Marta 3, I-50139 Firenze, Italy
2
INFM and Dipartimento di Fisica, Università di Roma “La Sapienza” P.le A. Moro 2, I-00185 Roma, Italy
3
INFM and International School for Advanced Studies (SISSA/ISAS) via Beirut 4, I-34014 Trieste, Italy
4
Laboratoire de Physique Théorique (UMR du CNRS 8627), Bâtiment 210 Université de Paris-Sud - 91405 Orsay Cedex, France
Received:
13
March
2003
Accepted:
16
June
2003
We study the asymptotic behaviour of the Bak, Tang, Wiesenfeld
sandpile automata as a closed system with fixed energy. We
explore the full range of energies characterizing the active
phase. The model exhibits strong non-ergodic features by settling
into limit-cycles whose period depends on the energy and initial
conditions. The asymptotic activity (topplings
density) shows, as a function of energy density ζ, a devil's
staircase behaviour defining a symmetric energy interval-set over
which also the period lengths remain constant. The properties of
the ζ-
phase diagram can be traced back to
the basic symmetries underlying the model's dynamics.
PACS: 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.65.+b – Self-organized systems / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EDP Sciences, 2003
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